System for interpolating surface potential values for use in calculating current density

ABSTRACT

A system for mapping and/or displaying spatiotemporal features of underlying event-related neural activity involves measuring the event-related evoked potential values at a limited number of points over the region of interest, deriving a first grid of potential values at points over the area of interest representing at least about a five fold increase in the number of points by a Kriging-type of spatial statistical interpolation, and using the first grid to derive for the region of interest a second grid of points of current density values by a Laplacian conversion. A plurality of second grids of current density values spaced apart in time are derived and displayed on a monitor in cartoon-type fashion to provide a cartoon-type display of the features of the event-related evoked response over the region of interest varying with time. Various other displays are possible for highlighting specific features.

This application is a continuation of application Ser. No. 07/382,622,filed on Feb. 23, 1989 now abandoned, which is a continuation-in-part ofapplication Ser. No. 07/085,971, filed Aug. 14, 1987 now abandoned.

FIELD OF THE INVENTION

This invention relates to electrophysiological measuring techniques forderiving features of underlying neural activity in humans and animals.

The invention will be described more specifically with reference to themapping and/or displaying of features of the current density at thesurface of the human scalp in response to auditory stimuli although itwill be apparent that the invention has broader application. Inparticular, the invention should similarly be applicable in cardiology,neurology and other situations where there is a practical limit to thenumber of probes or electrodes that can be used to study the currentdensity of underlying neural activity.

The invention involves both processes and apparatus for doing themapping and/or displaying.

BACKGROUND OF THE INVENTION

It has been known that cortical auditory evoked potentials (CAEP)elicited by speech sounds in humans generally exhibit characteristicwaveshapes and scalp topography in response to specific acousticfeatures of the sounds, such as onset of voicing (VOT) and place ofarticulation. Electrophysiologic assessment of peripheral, brainstem andcortical responses to sound in young high-risk infants indicate that oneor more levels of the auditory system may be involved in impairedauditory processing. Initial studies of language development in theseinfants also suggest that deviant cortical auditory processing in theyoung infant may be associated with poorer early language acquisitionthan infants with normal cortical responses to sound. So that possibleremedial action may be taken as early as possible, early detection ofimpaired auditory processing is important.

To increase the usefulness of these electrophysiological measures, it isdesirable to improve their specificity and sensitivity. To this end, forexample, there is needed an improvement in techniques for the analysisof the pattern of auditory event related potentials (AERP) to speech andnon-speech sounds.

It is known that the potentials recorded from the scalp derive fromvolume currents that originate in neuronal transmembrane currents withinthe brain. Active brain regions whose neurons are similarly oriented arecapable of generating volume currents of sufficient magnitude to passthrough the brain and its coverings, although markedly attenuated, wherethey are sensed as potential differences at the surface of the scalp.These volume currents must pass out of and back into the brain in orderto complete the electrical circuit required by the conservation ofcharge. A good deal of the current flow within the scalp, however, isparallel to this surface rather than transcranial. Thus, the potentialdifferences associated with lateral currents do not directly reflecttranscranial flow and serve to diffuse the recorded potentialdistributions at the scalp surface. It has been suggested that theLaplacian derivation, which is proportional to the second spatialderivative of the field potential, is a measure of the current flowperpendicular to the recording surface, and therefore, of transcranialcurrent flow. This measure provides a substantially more focusedestimate of the intracranial sources of electrical activity than doesthe field potential distribution. It is also essentially referenceindependent, an important consideration in interpreting topographicdata.

In practice it turns out that computation of the Laplacian requires areasonably accurate estimate of the actual potential surface. It hasbeen attempted to derive the Laplacian directly from the recordingelectrodes by a differential operator implemented by analog circuits inwhich the Laplacian at a particular point is derived as the average ofthe gradients from a number of surrounding recorded points. However,these direct analog attempts have not proven particularly successful inmapping an area because of the limited number of points available foruse in the computation. In these attempts, the points used have beenonly the points directly measured and practical reasons limit the numberof points that can be directly measured. In particular, the attempt todo such a Laplacian derivation directly with fifteen or twenty points,the limit generally thought practical to measure directly conveniently,has not proved satisfactory.

Similarly, in other electrophysiological processes involving theanalysis of the pattern of neural potentials in both humans and animals,there can be used to advantage better techniques for mapping and/ordisplaying such potentials.

SUMMARY OF THE INVENTION

To this end, I have found that it is possible to use effectively in theLaplacian derivation interpolated points to supplement the directlymeasured points, and thereby to have enough points to do an effectiveLaplacian derivation. In particular, by use of a statistical spatialinterpolation technique based on the probabilistic representation ofregionalized variables, there is derived a grid of points that definesover the area under investigation, a relatively smoothly varyingpotential surface that passes through all of the measured pointsavailable with good support between points and of which the subsequentLaplacian derivation provides a surface of current density that isgenerally consistent with the surface expected and in which the displayof features of interest is considerably improved. I have found itespecially advantageous to use a modification of a statistical contourestimation method employed in non-physiological applications, primarilygeological analysis, called "Kriging". This method has been developed toprovide optimal estimates of large area contours sampled by discrete,often unsystematic point observations and its theory is described in apaper by G. Matheron entitled "The Intrinsic Random Functions and TheirApplications" in Advances in Applied Probability, 1973, Vol. 5, pps.439-468 and at pages 44-75 in a book by B. D. Ripley, entitled "SpatialStatistics" in the series entitled "Probability and MathematicalStatistics, published by John Wiley, New York; 1981. This Kriging methodin its standard format has been programmed for use by a computer withvarious weighting procedures. For example, one form of Kriging softwareis commercially available from Golden Software of Golden, Colo. However,I have found that for use in electrophysiological processes of concernto the present invention, it is particularly advantageous to modify anordinary Kriging treatment that uses for the estimation a linearpolynomial to the 1.0 power (linear variogram), by using instead thesame polynomial to a power of between 1.4 and 1.8 (power functionvariogram), and preferably 1.8. It is an advantage of this interpolationmethod that it appears to be useful for any particular electrode arrayand essentially independent of the particular distribution of theelectrode array. Kriging of this kind has made possible transformationof a grid of fifteen points into a grid of almost fifteen hundredpoints.

The resulting three dimensional potential surface, in which the x and ycoordinates correspond to the x and y coordinates of the point in aflattened plane simulating the surface of interest and the z coordinateis the potential value, normally exhibits a diffuse and ratherfeatureless appearance. However, by use of a Laplacian transformation,for example, one involving a five point difference operator, there canbe generated a three dimensional Laplacian surface in which discretezones of outward (upgoing regions) and inward (downgoing) transcranialcurrents are clearly disclosed and are consistent with the results ofmore elaborate studies.

The five point difference operator serves as a discrete analogue to theLaplacian operator defined in multi-variable calculus. This five pointoperator yields an output that approximates the second spatialderivative. It will be convenient hereinafter to refer to the output ofa suitable discrete analogue of a Laplacian operator as an approximatesecond spatial derivative.

Summarizing, in an analysis in accordance with an illustrativeembodiment of the invention, the topographic data will be subjected to astatistical spatial interpolation technique (e.g. Kriging) and then totwo-dimensional current source density (Laplacian) analysis, so as todefine the spatial distribution of transcranial current flow that occursduring the processing of auditory information in each task. Thereafter,the Laplacian data can be examined for spatially stable peaks thatreflect circumscribed transcranial current flow associated withlocalized activation of specific cortical regions. The amplitude andtiming of these peaks will be measured to define the locus, timing andmagnitude of cortical activity associated with each task.

Moreover, because both Kriging and Laplacian transformation involvelinear operators, it is feasible to combine mathematically both suchoperations in a single operation, although the subsequent discussionwill be in terms of separate operations.

Moreover, for ease of interpretation, in a preferred embodiment myinvention further includes the conversion of each derived set of x, y, zdata points into a three dimensional perspective image that directlydisplays the profile of the variable of interest as height above theelectrode grid on the scalp surface. Moreover, by displaying successiveframes displaced in time in cartoon-display fashion, there can bedisplayed in three-dimensions the continuous evolution of the Laplaciansurface over the real- time auditory evoked potential period beingmeasured.

Additionally, to facilitate comparison of an individual case with agrand mean of representative normal cases and with a z- scoretransformation of the case data, the moving three dimensional Laplaciansurface generated for an individual case is displayed in one window of athree window monitor screen, the corresponding surface for the grandmean in a second window, and the z- score of the comparison in a thirdwindow.

Additionally, there may be displayed the Laplacian value of any pointincluding any original measuring point as it varies with time.

The invention will be better understood from the following more detaileddescription taken with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the outline of a head and the disposition of fifteenelectrodes over the head for collection of the electrophysiologicaldata, for further processing in accordance with the invention.

FIG. 2 shows a three-dimensional event-related-potential surface derivedfrom fifteen originally measured points after Kriging interpolation, asis characteristic of a typical embodiment of the data processingtechnique of the invention;

FIG. 3 illustrates the three-dimensional Laplacian current densitysurface derived from the potential surface shown in FIG. 2 in the mannercharacteristic of the invention;

FIG. 4 is a plot against time of both the potential and the currentdensity at a particular point that can readily be derived from the datashown in FIGS. 2 and 3; and

FIG. 5 is a block schematic of apparatus for use in an illustrativeembodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Before beginning the detailed description, some additional backgroundwill be helpful.

As is known, two basic problems confront the interpretation of thetopography of event-related potentials. First, two electrodes, an"active" and a "reference" are required in bioelectrode recordings.Scalp electrode sites are rarely inactive with respect to intracraniallygenerated potentials, and even noncephalic sites are not inactive withrespect to potentials generated within the auditory system, due to thevertical orientation of the active generators of auditory evokedpotentials. Therefore, potentials recorded from most scalp loci containcontributions from both the active and reference electrodes, so absolutepotential values are not generally obtainable. Identification of theintracranial generators of an observed potential distribution is furthercomplicated by the effects of the shape and impedance characteristics ofthe brain and its coverings. The volume conduction characteristics ofthe head lead to an extensive diffusion of currents that result inbroadly distributed field potentials at the surface of the scalp. Thus,it is often difficult to differentiate potentials generated even withinwidely spaced intracranial structures due to their extensive spatialoverlap at the scalp. These same considerations persist when there ismeasured a potential distribution at the surface of a human or animalsessentially anywhere along the surface.

The reference problem is generally solved by describing the surfacetopography in terms of potential gradients, usually defined empiricallyas the potential differences between adjacent scalp electrodes. Sincethe reference is common to both electrode linkages, any contribution itmight make to the potentials recorded at each site is canceled. However,this does nothing to reduce the broad scalp potential distribution dueto volume current spread. It has previously been proposed that thecomponent of volume current that flows laterally within the scalp itselfcan be eliminated by the use of a two dimensional current source density(Laplacian) method. This technique eliminates contributions to thesurface potential distribution from tangential current flow, yielding anestimate of the transcranial currents alone. Empirically, this methodprovides a striking sharpening of the observed electric events.

It is possible to obtain a crude estimate of the Laplacian distributionusing analog combinations of the observed potential values at eachelectrode. However, in implementing Laplacian analyses using a fivepoint differential operator, it is found that close point spacings areneeded to adequately estimate the second spatial derivative when baseddirectly on interelectrode gradients. Since optimally dense arraysrequire too many electrodes to be generally practical, I have soughtmethods for accurate interpolation of the observed potential valuesbetween electrodes so the Laplacian could be calculated using theinterpolated voltages. Since the surface potential gradients areaffected by generator size and depth, there is no fixed formula foraccurate interpolation. Specifically, linear and inverse distancesquared interpolations commonly used in mapping applications tend not tofit accurately observed physiological surface distributions.Additionally, various other interpolation techniques such as splininghave proved relatively ineffective in providing meaningful results.Accordingly, in accordance with an illustrative embodiment of theinvention, as mentioned earlier, there is advantageously employed astatistical contour estimation method employed previously only innon-physiological applications, i.e., geologic and geographic analyses.Specifically, the method called "Kriging", referenced above, has beendeveloped to provide optimal estimates, based on a global rather thanlocal fit, of large area contours sampled by discrete, oftenunsystematic, widely spaced point observations. In particular, I haveused Kriging to estimate a relatively dense rectangular grid ofpotential values that is a numerical representation of a threedimensional potential surface of a relatively small scale. The grid is anumerical matrix whose elements are measurements of the Z variable madeat points identified by the two rectangular planar coordinates X and Y.This grid of voltage values in turn is used in the Laplacian derivationto provide a similarly dense rectangular grid of current density valuesthat is a numerical representation of the current density surface ofprimary interest.

Although this method will not correct failures to sample major featuresof the original ERP field distribution because they occur betweenelectrode positions, Kriging can provide very satisfactoryrepresentation of ERP amplitude contours, with satisfactorily convenientelectrode density.

Kriging has been used in the geosciences to estimate values of a largearea surface at the nodes of a rectangular grid from irregularly widelyspaced sample data points. Kriging involves a number of levels, two ofwhich, universal and ordinary Kriging, are most relevant for myinvention. Ordinary Kriging will be discussed more fully below inconnection with an exemplary embodiment. Of possible interest also isthe more general universal Kriging. Universal Kriging makes optimal useof autocorrelation between points on a surface and like ordinary Krigingrequires an approximation of the spatial autocorrelation between sampledata points before contouring is begun. As will appear below, thedifference is that ordinary Kriging assumes the absence of any fixedtrend underlying the data whereas universal Kriging incorporates afixed, or deterministic, underlying trend. In other words, ordinaryKriging is universal Kriging in which the trend model is not apolynomial or some other higher order function, rather, the underlyingtrend is a constant, i.e., a flat plane. The universal Kriging optionwill be more appropriate when denser electrode arrays are used, and/or abetter understanding of the actual underlying neural activity isavailable.

Each of these forms of Kriging involves the use of a variogram, which isa function relating the covariance of the difference between points, tothe distance between the points and an important parameter to beselected is the form and the order of the variogram.

As discussed more fully in a paper entitled "Automatic Kriging andcontouring in the presence of trends (Universal Kriging Made Simple)"published in the Journal of Canadian Petroleum Technology by M. W. D.Davis and M. David, Vol. 17, No. 1 January-March, 1978, the role ofKriging is defined as follows. Given a series of values Z (x_(i)) knownat a series of points x₁, x₂, . . . x_(n), what are the best weights λ₁,λ₂, . . . λ_(n) to be applied to the known values in order to obtain theestimated value Z (x), i.e. the interpolated value desired, at any pointx where the information is desired, ##EQU1## A usually accepted criteriaof goodness of fit is the sum of squared differences between the realand the estimated values. The geostatiscal theory of Matheron allows thecalculation of this sum of squares (variance of the estimation error) asa function of the data points only, plus a model. This model is toconsider the phenomenon under study as one realization of a randomprocess in the plane.

Conceptually, let us divide the surface Z (x) into a trend and afluctuation

    Z (x)=m (x)+ε(x).

where trend m is a large - scale variation regarded as fixed, and thefluctuation ε is a small-scale random process. We will assume that thecovariance function C (x, y) is known, and no stationarity condition isneeded, as will be discussed more fully below. The C is the covariancefunction of ε as well as of Z.

The importance of the above formula is that the two components arepredicted separately. For a smooth summary, there is used

    Z (x)=m (x)

whereas for interpolation

    Z (x)=m (x)+ε (x)

where " " indicated a predicted value and " " is the approximationsymbol.

A first condition added to the model is that the random function behomogeneous i.e. there is no systematic trend in the distribution, alsoknown as stationarity. Then it is possible to define a variogram of thephenomenon and to express the variance of the estimation error as afunction of this variogram. Having an expression for the variance, it ispossible to minimize it with respect to the weighting coefficients usedat each point. This is usually defined as ordinary Kriging, a variationof which is involved in my presently preferred form of the invention.

However, further enhancement of the desired characteristics may beachieved by universal Kriging in which the variogram and the trend aremore closely fitted to the known characteristics of the data byselection of mathematical expressions for these terms which incorporatewhat is known about the underlying neural activity.

There now will be developed the ordinary Kriging equations for theoptimal weights, λ_(i) and the minimum mean square error; given that thecovariance, cov(v) is known and the mean is assumed to be constant,where v=u₁ -u₂, i.e., the difference between the points u₁ and u₂.

The mean square error of estimation or estimation variance equation isgiven by ##EQU2##

To find the set of weights that give the minimum mean square error(MSE), the expression on the right of the above equation must beminimized subject to the constraint that all the weights add to 1(unbiased)

This set of weights is given by solving the following set of (n+1)linear equations in n weights λ1, and the Lagrange multiplier μ.##EQU3##

The solution gives the optimal weights which will be denoted λ_(i) *.

The minimum MSE, σ_(p) ² * is derived to be ##EQU4##

An important element of this approach is the selection of an appropriatevariogram to model the known spatial characteristics of the phenomenonbeing investigated. The variogram is generally described as follows.Consider two real numerical values Z (x) and Z(x+h) at two points x and(x+h) separated by the vector h. The variability between these twoquantities is characterized by the variogram function 2γ(x,h), which isdefined as the expectation (E), or mean, of the random variable[Z(x)-Z(x+h)]², i.e. 2γ(x,h)=E{[Z(x)-Z(x+h)]² }. This model should beone that yields results consistent with results known to be accuratebased on earlier experience. This generally requires that the variogrammodel chosen be one which provides parabolic behavior of the variogramat small separation distances and whose parameters yield a surface whichpasses smoothly through all the data points with maximum support betweenthe data points.

A variogram model found to satisfy these requirements for the situationunder study is

    γ(h)=wh.sup.b

where the slope (w) is one and the exponent (b) is chosen appropriately.As previously mentioned, programs for carrying out ordinary Kriging inwhich the exponent value (b) above is one, are commercially available,e.g. Golden Software.

I have found that it is particularly advantageous in the embodiments ofmy invention being described to use ordinary Kriging in which thevariogram model uses a value of (b) between 1.4 and 1.8, and mostadvantageously 1.8.

In the above set of ordinary Kriging equations the chosen variogram withthe appropriate parameter values can be substituted into the estimationvariance equation for the term cov(u_(i) -u₂) to obtain the desiredresults.

A specific example, in accordance with the above treatment, of ordinaryKriging using the specific variogram model set forth above, for thepreferred value of 1.8 as the power of the power function, follows.

A set of 15 electrodes, as seen in FIG. 1, is used to derive, at a giveninstant in time, an interpolated surface of potential values.

The interpolated surface is defined by a regular grid of points; thisgrid has 23 rows by 63 columns for a total of 1,449. A value at each andevery grid point is computed as a weighted average of the 15 electrodemeasurements available: ##EQU5## where Z_(k) .tbd.is the interpolatedvalue at grid location "k".

λ_(i),k .tbd.is the weight associated with electrode measurement "i"when estimating grid location "k".

Z_(i) .tbd.known electrode measurement "i".

The weights used to interpolate the value at grid location "k" areunique to grid location "k"; that is, a different set of weights must becalculated for every grid location. The weights used to interpolate thevalue at grid location "k" are functions of the various separationdistances between pairs of the 15 known electrode measurements, and thevarious separation distances between the 15 known electrode measurementsand the grid location "k".

The weights are generated by solving the following set of 16 linearequations involving 16 unknowns. The 16 unknowns are comprised of the 15weights plus a "lagrange multiplier". This last term the lagrangemultiplier) is included for mathematical convenience and is not used inthe computation of the interpolated value.

The Kriging weights for interpolating the value at grid location "k" aregenerated by solving, in the equivalent matrix form, the followingsystem of linear equations: ##EQU6## where d_(ij) .tbd.the distancebetween electrode "i" and electrode "j".

λ_(i) .tbd.weight associated with electrode "i".

μ.tbd.lagrange multiplier.

d_(io) .tbd.the distance between electrode "i" and the grid location.

The various equations described above are found derived in variouspublications in geostatistics including a book entitled "RandomFunctions and Hydrology" pps. 385-412 by R. L. Bras and I.Rodriguez-Iturbe-Addison Wesley Publishing Co., Reading, Mass. and in abook entitled "Mining Geostatistics" Academic Press, N.Y. (1978) by A.G. Journel and Ch. J. Juijbregts. Similar sets of equations and theirmatrix equivalents for the more general universal kriging can be foundin these same references.

Once a set of weights has been derived for a given configuration ofelectrodes, this set of weights can be used for any subsequent Kriginginterpolation from the same electrode configuration with substantialincrease in efficiency.

In FIG. 1, as a close subset of the International 10-20 Convention thereare shown the sites of the fifteen electrodes, distributed as indicatedon the outline of the head shown by the solid circle. The electrodes areshown associated with the rectangle overlying the circle, and thisrectangle essentially corresponds to a flattening of the scalp surfaceof interest. Based on the voltages measured at each of these electrodes,Kriging interpolation in the manner described above is used to derivethe three dimensional contoured potential surface, shown in FIG. 2, forthe portion of the head included within the rectangle, viewed from therear, above and slightly to the right of the dotted midline shown inFIG. 1.

A reference electrode, not shown, would be placed in a relativelyinactive area, for example, the back of the head. The exact position ofthe individual recording electrodes is not critical and is generallydictated by the task being evaluated and by experience, although it isadvantageous to locate electrodes over regions where current generationis expected. Moreover, the particular number, 15, is not critical thoughfound a reasonable compromise between sufficient samples for a goodestimation and the complexity increase as the number of samples isincreased.

In other tasks, a different number of electrodes may represent a bettercompromise. The invention should prove useful even when as few as fourrecording electrodes are used for the particular task in mind.

To achieve the surface depicted, Kriging using a variogram to the 1.8power, as discussed above, is used to define a rectangulartwo-dimensional grid of 63 points by 23 points, each corresponding to Xand Y coordinates of interest and for each grid point there is provideda potential value. There is provided such a grid for each complete setof potential points measured at a given time. Typically, 128 such gridsfor 128 sets have been calculated, spaced apart in time one samplinginterval, typically 6.24 milliseconds, corresponding to an analysis timeof about 800 milliseconds for a complete cycle or epoch.

To facilitate the ease of observation, the two dimensional grid ofpoints, each of an appropriate magnitude, is transformed to a threedimensional contoured surface of the kind shown in FIG. 2 by techniquesnow familiar in image processing for special effects, in which the thirdz dimension, or height, represents the voltage at the point having thecorresponding X and Y coordinates. The image processing technique isused to provide a perspective view.

More particularly, FIG. 2 shows a plot of the potential surfaceresulting from one such grid of 63 points by 23 points. In particular,it is to be noted that the potential surface is relatively smoothlyvarying and passes through all of the measured points available withgood support between points, as is needed to provide, after theLaplacian transformation, a surface of current density consistent withwhat is expected from established measuring techniques.

This is in contrast to the interpolation by distance-weighted averagetechniques which results in products in which most data pointsconsidered show up as local maxima or spikes.

The evoked potential data depicted in FIG. 2 is now further processed bya five point differential operator to obtain a "Laplacian map". TheLaplacian map provides a direct estimate of the magnitude of currentflowing perpendicular to the surface of the scalp and thus, thedistribution of currents passing into and out of the brain at each pointin space. In FIG. 3 there is shown the Laplacian current topographyapproximating the second spatial derivative of the interpolatedpotential surface shown in FIG. 2. As can be seen from comparison of thepotential and current flow topographies shown in the two figures, theLaplacian mapping provides a sharper spatial resolution of the currentflow features, since the elimination of potential gradients due totangential extracranial current flow permits the localization of thoseportions of the extracranial currents attributable to generators withinthe brain. In particular, it is to be noted that the Laplacian mappinghighlights features of interest not immediately obvious from thepotential surface and significantly eases the problem of distinguishingthe features of interest. Transcranial current flow maxima can bereadily identified visually from a live computer cartoon-type sequentialdisplay of the spatiotemporal mappings. This defines the location andtiming of peak current flows for concentrated study.

The amplitude and latency of each peak may be employed as the measuresof timing and magnitude of processing within a particular brain region.Topographic data obtained from infants and adults has permitted thedelineation of two major intracranial generators of the auditory evokedrelated potentials that correspond to peaks in the ERP topography, onelocated within the superior temporal plane projecting fields toward theparamedian frontocentral scalp, and another within the lateral surfaceof the superior temporal gyrus that projects to the immediatelyoverlying temporal scalp illustrated in FIG. 3.

Data from auditory processing tasks that require both acoustic andsemantic analysis indicates the presence of a third, more posteriorgenerator that is active during semantic processing. Thus, four distinctcurrent maxima, two from each hemisphere, are present when acousticprocesses alone are activated, whereas additional maxima may be presentwhen semantic processing is required. Should the Laplacian of morecomplex linguistic tasks provide evidence for further differentiation ofregional cortical generators, these additional current maxima can alsobe measured in the same manner as described.

In tests which have been conducted, the improved spatial resolutionprovided by Laplacian analysis has increased the validity of peakamplitude measurements, since spatial overlap of field distributionsfrom adjacent intracranial generators is reduced. The proposed method ofpeak identification and measurement also substantially reduces thenumber of quantitative variables required to define the spatiotemporalevent-related-potential distributions, and increases the power ofstatistical comparisons.

The specific results depicted involved ordinary Kriging. As mentionedabove, universal Kriging can provide improved interpolation when moremeasured data points are available and/or when there can be usedknowledge of the underlying neural activity. Universal Kriging permitsthe incorporation of knowledge about electric potential fields and abouthuman and animal electrophysiology into the expressions for thevariogram and the deterministic trend term characteristic of universalKriging as discussed previously.

Definition of the timing of each current maximum has permittedconfirmation of inferences on the role of the underlying neural activityin stimulus information processing. Thus, for example, potentials thatreflect acoustic processing precede those associated with semanticprocesses and arise from different brain regions. Further, peaks whoselatency exceeds that of a behavioral response can be excluded fromconsideration as manifestations of the discriminative process.

For use by a clinician, the process described typically would beemployed for each of the 128 sampling intervals to provide a set of 128frames each showing a Laplacian surface of the kind shown for theparticular sampling interval. It is feasible to use the same set ofweights, originally derived for the first frame, for the remainingframes. If each of these frames is displayed in turn on a televisionmonitor at an appropriate rate, there is achieved a cartoon-like movingdisplay of the Laplacian surface with the peaks shown rising and fallingto simulate the spatial pattern of focal current generation changesthrough time.

It is, of course, desirable to compare visually such changes of anindividual case under study with a norm to detect any dysfunction. Tothis end, there is again derived 128 grids, each including 63 points by23 points in which the magnitude of each point is derived as the grandmean of a cohort of normal cases, typically at least fifteen, derived inthe manner described and from these grids there are also derived 128frames of Laplacian surface of the kind shown in FIG. 3. Thereafter,either in a separate television monitor or in a separate window in amultiwindow monitor the two cartoon-like displays can be viewed insynchronism side by side for comparison.

Moreover, in some instances it will be desirable to display in the sameway simultaneously the z- score of corresponding points in an individualcase grid where in the usual fashion the z score of a point in the zgrid is defined as the magnitude at that point in the Laplacian grid ofthe individual case minus the magnitude at that point in the Laplacianmean grid, divided by the standard deviation calculated in the usualfashion for that point in the standard deviation grid calculated fromthe distribution of normal case Laplacian grids. In this way there maybe simultaneously displayed a surface in which the elevation of a pointin the surface corresponds to the z-score of that point in the scalp atits particular time frame.

In familiar fashion, provision can be included for freezing a time frameof the displays for closer inspection or for slowing or speeding of therate of change of the potential at the scalp. In particular, it ispossible to collect from each of the 128 sampling intervals both thepotential value and the current density (Laplacian) value at aparticular point of the surface, for example, a point corresponding tothe location of any selected one of the fifteen electrodes used fortaking the potential measurements, and these values may be plottedagainst time for displaying the change with time of the potential valueand the current density at the selected points.

In FIG. 4, which is such a display, there are shown temporal waveformsat electrode C3M of the current density C and of the original potentialP. It will be noted that the current density waveform C highlightsfeatures not readily discerned in the original potential waveform P.Such a representation is of particular value as an analytical tool tothe investigator, because it is a concise summary of the parameters ofinterest.

In FIG. 5, there is shown in block schematic form the basic elements ofapparatus suitable for carrying out the processing described.

The first block 30 included represents the electrode array positionedappropriately in the area under study. In humans, this typically will beon the skin surface. In animals, these may also be in an interior area.

The signals derived by the electrodes typically are very weak and so arefirst amplified before further processing. It is then usuallyadvantageous to sample the individual continuous wave analog signalsfrom each electrode, typically into 128 samples, for the time expectedfor one epoch of the evoked potential wave in the area under study andeach sample is digitized in binary code. Since the signals are notusually processed in real time, the various digitized samples of thevarious electrodes will be stored in sequence in a suitable storagemedium, either a tape or disk. Typically, the stimulus will be repeateda number of times and the average of the successive values for anindividual electrode used in the usual fashion to reduce the signal tonoise ratio, based on the fact that random noise will average out whilethe signal will build up cumulatively. This processing is represented bythe signal processor block 32 shown supplied by the leads from thevarious electrodes of array 30.

The output of the signal processor 32 is shown supplied to a memory 34where the digitized samples at each electrode for each sampling intervalare stored for access when desired. The output of the memory as neededis supplied to a microprocessor 36 programmed to do the Kriging of thedigitized samples derived from the fifteen electrodes into a grid of 63points by 23 points as described, extra points being provided aspreviously discussed to compensate for edge points to be lost.Generally, it will be desirable to store the values of 128 grids,corresponding to one for each of the 128 sampling intervals, in a memory38 as depicted.

The various grid values are supplied as needed from the memory 38 to amicroprocessor 40 programmed to do the five point differential Laplacianconversion, previously discussed, to derive for each of the 128 grids acorresponding grid each of 61 points by 21 points, assuming provisionhas been made for the extra points being lost, as discussed above.Essentially, the five point differential operation amounts to taking theaverage of the sum of four differences, each corresponding to thedifference of the value at a center point from the value at each of fourproximate surrounding points. The four points may comprise the twopoints on the same horizontal line on opposite sides of the point beinginterpolated plus the two points on the same vertical line on oppositesides of the point being interpolated. Alternatively, the points may bethe four closest points around the central point on diagonals throughthe central point. There is then similarly stored the values of 128grids, one for each sampling interval in a memory 42 for use as neededin the signal processor 44, which uses the signals stored in memory 42to develop for each of a 128 grids of values a grid of values that canbe scanned to produce, in perspective, a surface of the kind depicted inFIG. 3.

Of course other number and arrangements of points can be used for theLaplacian derivation, as is familiar to workers in the art.

The output of the signal processor 44 along with the grids of the grandmeans stored in store 46 and the Z-scores calculated in signal processor48 are supplied, appropriately synchronized, to three separate windows50A, 50B and 50C of the screen monitor 50. The z-score processor 48 alsoneeds to be supplied with information about the Laplacian grids of theindividual case, available from memory 42, and information about thegrand mean Laplacian grids, available from store 46.

Additionally, for a display as shown in FIG. 4; there can be derivedfrom memory for any particular point of the grid the values of potentialand current density for each successive sampling interval.

It can be appreciated that various modifications can be made in thebasic system described without departing from the spirit and scope ofthe invention. In particular, the Kriging technique can be used tointerpolate any desired number of points between two given points. It isgenerally important for a marked advantage in the subsequent Laplacianderivation to obtain at least about a tenfold increase in the totalnumber of points, corresponding to about a threefold increase in each ofthe x and y dimensions. However, obviously any increase in the number ofpoints can effect an improvement and there may be instances where asmaller increase will suffice.

Moreover, as was previously indicated, the specific process describedcan be used for mapping the current density distribution in variousother parts of the body. Generally, each such task will involve theplacement of a suitable number of electrodes in appropriate positionsrelated to the task. As a consequence, other forms of variograms may bepreferred for the Kriging.

By the use of this technique, together with appropriate positioning ofparticular electrodes to emphasize particular electrophysiologicresponses, there can be derived a wide variety of data to pinpoint thetiming and locus of underlying neural activity.

There accordingly will be provided a better means for directlyidentifying the presence and spatiotemporal characteristics ofelectrophysiological activity in individual subjects.

I claim:
 1. A process for deriving the current density at points over anarea of interest as a measure of the underlying neural activitycomprising:the step of measuring physiological potentials at a limitednumber of points over the area of interest by means of electrodes toyield electrical signals indicative thereof; the step of using theelectrical signals to estimate the potential at each of an increasednumber of points over the area of interest by Kriging interpolation ofthe measured potentials; and the step of deriving from said estimatedpotentials a current density value at each of said points.
 2. Theprocess of claim 1 in which the Kriging interpolation is ordinaryKriging.
 3. The process of claim 1 in which the Kriging interpolation isordinary Kriging with a power function variogram model.
 4. The processof claim 3 in which the variogram is used with a power function raisedto between 1.4 and 1.8.
 5. The process of claim 1 in which the Kriginginterpolation is universal Kriging utilizing information available as tothe underlying neural activity in the area of interest.
 6. The processof claim 1 wherein the step of Kriging interpolation and the step ofderiving current density values are calculated in a single step.
 7. Theprocess of claim 6 wherein the single step is performed by amicroprocessor.
 8. The process of claim 1 wherein the estimating stepand the deriving step is performed by a microprocessor.
 9. The processof each of claims 1, 2, 3, 4, and 5 in which the current density iscalculated from a Laplacian transformation of said estimated pointpotentials.
 10. The process of each of claims 1, 2, 3, 4 and 5 in whichthe step of deriving the current density involves a five pointdifference operator to approximate a second spatial derivative at eachpoint.
 11. The process of each of claims 1, 2, 3, 4, and 5 in which saidKriging interpolation generates at least about a five fold increase inthe number of points.
 12. Apparatus for displaying the features ofunderlying neural activity over an area of interest comprising:means formeasuring physiological potentials at a plurality of points and forgenerating electrical signals indicative thereof; a first electronicmeans for processing said signals to derive a grid of estimatedpotential values, corresponding to the area of interest, of increaseddensity by a Kriging interpolation program; a second means forprocessing said grid of estimated potential values to derive acorresponding grid of current density values; and means for displayingin perspective a three dimensional image representing said grid ofcurrent density values and displaying thereby the current densityfeatures of underlying neural activity over the area of interest. 13.The apparatus of claim 12 in which the electronic means for processingsaid grid of estimated potential values uses a Laplacian transformationto derive a corresponding grid of current density values.
 14. Theapparatus of claim 12 in which the electronic means for processing saidgrid of estimated potential values uses a five point difference operatorto derive a corresponding grid of current density values.
 15. Theapparatus of claim 12 in which the interpolation is ordinary Kriging.16. The apparatus of claim 12 in which the interpolation is universalKriging.
 17. The apparatus of claim 12 in which the Kriginginterpolation is ordinary Kriging with a power function variogram model.18. The apparatus of claim 17 in which the variogram is used with apower function raised to between 1.4 and 1.8.
 19. Apparatus fordisplaying features of underlying neural activity over an area ofinterest comprising:an electrode array positioned over the area ofinterest for measuring potentials at a corresponding number of pointsover such area and means for generating electrical signals indicativethereof; signal processing means for providing interpolated values by aKriging interpolation program of potentials at points intermediatebetween said corresponding numbers of points for providing an increasednumber of potential values; signal processing means for deriving asubstantially corresponding number of current density values for thearea of interest; and means for displaying the current density values asa perspective three dimensional display of the current density valuesover the area of interest.
 20. Apparatus in accordance with claim 19 inwhich said Kriging program utilizes ordinary Kriging.
 21. Apparatus inaccordance with claim 19 in which said Kriging program is a universalKriging interpolation.
 22. The apparatus of claim 19 in which theKriging interpolation is ordinary Kriging with a power functionvariogram.
 23. The apparatus in accordance with claim 22 in which thevariogram is used with a power function raised to between 1.4 and 1.8.24. The apparatus of claim 19 in which the Kriging interpolation isuniversal Kriging.
 25. The apparatus of claim 19 in which the signalprocessing means derives the current density by performing a Laplaciantransformation.
 26. The apparatus of claim 19 in which the signalprocessing means derives the current density by using a five pointdifference operator.
 27. Apparatus for displaying features of underlyingneural activity at a desired point in an area of interest on a human oranimal comprising:a plurality of electrodes for positioning at pointsover the area of interest and means for deriving therefrom electricalsignals as measures of the physiological potentials at such points; afirst electronic means to derive by a Kriging interpolation program agrid of estimated potential values of an area corresponding to the areaof interest with a greater coordinate density than the number oforiginal points; a second electronic means for processing said grid ofestimated potential values to derive a corresponding grid of currentdensity values; means for sampling the values of a selected point in thegrid of estimated potential values and the grid of current densityvalues corresponding to the desired point; and means for displaying saidsampled values of the estimated potential and of the current density atthe desired point in successive sampling intervals in a plot againsttime.
 28. Apparatus in accordance with claim 27 in which the pluralitycomprises fifteen electrodes.
 29. The apparatus of claim 27 in which theKriging interpolation is ordinary Kriging.
 30. The apparatus of claim 27in which the Kriging interpolation is ordinary Kriging with a powerfunction variogram model.
 31. The apparatus of claim 30 in which thevariogram is used with a power function raised to between 1.4 and 1.8.32. The apparatus of claim 27 in which the Kriging interpolation isuniversal Kriging.
 33. The apparatus of claim 27 in which the signalprocessing means derives the current density by performing a Laplaciantransformation of said grid points.
 34. The apparatus of claim 27 inwhich the signal processing means derives the current density by using afive point difference operator to approximate a second spatialderivative at each grid point.
 35. Apparatus for displaying features ofunderlying neural activity over an area of interest of a human or animalbody comprising:means for measuring physiological potentials at aplurality of points and for generating electrical signals indicativethereof; a first signal processing means for deriving by a Kriginginterpolation for the area of interest, potential values at a grid ofpoints of a density greater than the measured points; a second signalprocessing means for deriving current density values at said grid ofpoints; and means for displaying the current density values at points inthe area of interest.
 36. Apparatus in accordance with claim 35 in whichthe means for displaying current density values at points in the area ofinterest displays said values at successive sampling intervals wherebythere is a dynamic display of the current density values with changingtime.
 37. The apparatus of claim 35 in which the Kriging interpolationis ordinary Kriging.
 38. The apparatus of claim 35 in which the Kriginginterpolation is ordinary Kriging with a power function variogram model.39. The apparatus of claim 38 in which the variogram is used with apower function raised to between 1.4 and 1.8.
 40. The apparatus of claim35 in which the Kriging interpolation is universal Kriging.
 41. Theapparatus of claim 35 in which the signal processing means derives thecurrent density by performing a Laplacian transformation of said gridpoints.
 42. The apparatus of claim 35 in which the signal processingmeans derives the current density by using a five point differenceoperator.
 43. The apparatus of claim 35 wherein the first signalprocessing means and the said second signal processing means comprises amicroprocessor.
 44. Apparatus for displaying features of underlyingneural activity over an area of interest comprising:means for measuringphysiological potentials at a plurality of points and for generatingelectrical signals indicative thereof; a first electronic means forprocessing said signals to derive a grid of estimated potential values,corresponding to the area of interest, of increased density by a Kriginginterpolation program; a second electronic means for processing saidgrid of estimated potential values to derive a corresponding grid ofcurrent density values; and means for displaying in perspective a threedimensional image representing said grid of estimated potential valuesand displaying thereby potential features of underlying neural activityover the area of interest.
 45. The apparatus of claim 44 in which theKriging interpolation is ordinary Kriging.
 46. The apparatus of claim 44in which the Kriging interpolation is ordinary Kriging with a powerfunction variogram model.
 47. The apparatus of claim 46 in which thevariogram is used with a power function raised to between 1.4 and 1.8.48. The apparatus of claim 44 in which the Kriging interpolation isuniversal Kriging.
 49. The apparatus of claim 44 in which the signalprocessing means derives the current density by performing a Laplaciantransformation of said grid points.
 50. The apparatus of claim 44 inwhich the signal processing means derives the current density by using afive point difference operator.
 51. The apparatus of claim 12, 27 or 44wherein the said first electronic means for deriving a grid of estimatedpotential values and the said second electronic means for deriving saidgrid of current density values comprises a microprocessor.